1. Two roads intersect at an angle of 52.7 degrees, with a field in between. A girl is walking on one of the roads 1.5miles from their intersection. Her house lies 0.85 miles from the intersection along the other road. If she cuts across the field to her house, how much walking mileage will she save?

Answer 1

The distance along the road is 1.5 + .85 = 2.35 mi

Using the law of cosines, the distance across the field is given by

d^2 = 1.5^2 + .85^2 - 2(1.5)(.85)cos52.7
= 1.427
d = 1.19 mi

So, she will save 2.35 - 1.19 = 1.16 mi

Answer 2

thanks